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|Title: ||Towards universal quantum computation in continuous-variable systems|
|Authors: ||Milne, Darran F.|
|Supervisors: ||Korolkova, Natalia|
|Issue Date: ||30-Nov-2012|
|Abstract: ||In this thesis we explore the possibility of creating continuousvariable
quantum systems that are capable of supporting universal
quantum computation. We begin by examining the measurement-based
model, which employs sequences of measurements on highly entangled
resource states, known as a cluster states. We suggest a method for
the construction of Gaussian cluster states based on ensembles of atoms
and quantum non-demolition interactions. We then go on to expand
our model to allow for the inclusion of light modes as part of the cluster.
This yields a new class of states, the composite cluster states.
This leads us to propose a new architecture for the measurement-based
model that uses these composite clusters to increase resource e ciency
and reduce computational errors.
The second part of this thesis concerns topological quantum computation.
In states exhibiting topological degrees of freedom, quantum
information can be stored as a non-local property of the physical system
and manipulated by braiding quasiparticles known as anyons. Here
we show how these ideas can be extended to continuous variables. We
establish a continuous variable analogue of the Kitaev toric code, show
that excitations correspond to continuous versions of Abelian anyons
and investigate their behaviour under the condition of nite squeezing
of the resource state.
Finally, we expand our continuous variable topological model to
include non-abelian excitations by constructing superpositions of CV
toric code anyons. We derive the fusion and braiding behaviour of
these non-abelian excitations and nd that they correspond to a CV
analog of Ising anyons. Using these resources, we go on to suggest
a computational scheme that encodes qubits within the fusion spaces
of the CV Ising anyons and derive one- and two-qubit quantum gates
operations that are implemented in a topological manner.|
|Publisher: ||University of St Andrews|
|Appears in Collections:||Physics & Astronomy Theses|
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